---
title: "Benchmarking Sparse Matrix Market Write Operations"
author: "Rohit Goswami"
date: "2023-11-03"
output: rmarkdown::html_vignette
vignette: >
%\VignetteIndexEntry{Benchmarking Sparse Matrix Market Write Operations}
%\VignetteEngine{knitr::rmarkdown}
---
## Introduction
This vignette demonstrates a benchmark comparing the `writeMM` function from the
`Matrix` package against the `write_fmm` function from the `fastMatMR` package.
Since `Matrix` does not support reading or writing dense matrices, we focus on
the sparse case.
## Loading Packages
First, we load the necessary packages:
```r
library(Matrix)
library(fastMatMR)
library(microbenchmark)
library(ggplot2)
```
## Benchmarking with Fixed Sparsity
We first benchmark for varying matrix sizes with fixed sparsity.
```r
# Function to create a sparse matrix of given size
create_sparse_matrix <- function(n, sparsity = 0.7) {
mat <- matrix(0, nrow = n, ncol = n)
for (i in 1:n) {
for (j in 1:n) {
if (runif(1) > sparsity) {
mat[i, j] <- rnorm(1)
}
}
}
return(Matrix(mat, sparse = TRUE))
}
# Define a range of matrix sizes
sizes <- c(10, 100, 500, 1000)
# Prepare data frame to store results
results_fixed_sparsity <- data.frame()
# Benchmarking
for (n in sizes) {
message("Benchmarking for matrix size: ", n, "x", n)
# Generate a sparse matrix of size n x n
testmat <- create_sparse_matrix(n)
# Run the benchmarks
bm <- microbenchmark(
Matrix_writeMM = writeMM(testmat, "mat.mtx"),
fastMatMR_write_fmm = write_fmm(testmat, "fmm.mtx"),
times = 10
)
bm$size <- n
results_fixed_sparsity <- rbind(results_fixed_sparsity, bm)
}
#> Benchmarking for matrix size: 10x10
#> Benchmarking for matrix size: 100x100
#> Benchmarking for matrix size: 500x500
#> Benchmarking for matrix size: 1000x1000
```
This is shown visually represented below:
```r
# Plotting
suppressWarnings(print(
ggplot(results_fixed_sparsity, aes(x = size, y = time, color = expr)) +
geom_point() +
geom_smooth(method = "loess") +
scale_y_log10() +
ggtitle("Benchmarking writes with fixed sparsity for 70% sparsity") +
xlab("Matrix Size") +
ylab("Time (ns, log10)")
))
#> `geom_smooth()` using formula = 'y ~ x'
```
## Benchmarking with Varying Sparsity
Now, we benchmark for varying sparsity patterns on a large matrix.
```r
# Sparsity levels to test
sparsity_levels <- seq(0.4, 0.95, by = 0.05)
# Prepare data frame to store results
results_varying_sparsity <- data.frame()
# Benchmarking
for (sparsity in sparsity_levels) {
message("Benchmarking for sparsity level: ", sparsity)
# Generate a sparse matrix of size 500 x 500 with varying sparsity
testmat <- create_sparse_matrix(500, sparsity)
# Run the benchmarks
bm <- microbenchmark(
Matrix_writeMM = writeMM(testmat, "mat.mtx"),
fastMatMR_write_fmm = write_fmm(testmat, "fmm.mtx"),
times = 10
)
bm$sparsity <- sparsity
results_varying_sparsity <- rbind(results_varying_sparsity, bm)
}
#> Benchmarking for sparsity level: 0.4
#> Benchmarking for sparsity level: 0.45
#> Benchmarking for sparsity level: 0.5
#> Benchmarking for sparsity level: 0.55
#> Benchmarking for sparsity level: 0.6
#> Benchmarking for sparsity level: 0.65
#> Benchmarking for sparsity level: 0.7
#> Benchmarking for sparsity level: 0.75
#> Benchmarking for sparsity level: 0.8
#> Benchmarking for sparsity level: 0.85
#> Benchmarking for sparsity level: 0.9
#> Benchmarking for sparsity level: 0.95
```
Now we can plot this:
```r
ggplot(results_varying_sparsity, aes(x = sparsity, y = time, color = expr)) +
geom_point() +
geom_smooth(method = "loess") +
scale_x_log10() +
scale_y_log10() +
ggtitle("Benchmarking writes with varying sparsity for 500 entries") +
xlab("Sparsity Level (log10)") +
ylab("Time (ns, log10)")
#> `geom_smooth()` using formula = 'y ~ x'
```
## Conclusions
Clearly, for larger matrices, and `fastMatMR` is consistently around two orders
of magnitude faster than `Matrix`. For extremely small matrices (<50) and at
high (~.7) levels of sparsity, the difference is not as pronounced, but for
matrices larger than 50x50 `fastMatMR` retains an order of magnitude
improvement.
## Session Info
This vignette was computed in advance, with the corresponding session info:
```r
sessionInfo()
#> R version 4.3.1 (2023-06-16)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: Arch Linux
#>
#> Matrix products: default
#> BLAS: /usr/lib/libblas.so.3.11.0
#> LAPACK: /usr/lib/liblapack.so.3.11.0
#>
#> locale:
#> [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
#> [3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
#> [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
#> [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
#> [9] LC_ADDRESS=C LC_TELEPHONE=C
#> [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
#>
#> time zone: Iceland
#> tzcode source: system (glibc)
#>
#> attached base packages:
#> [1] stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] ggplot2_3.4.4 microbenchmark_1.4.10 Matrix_1.5-4.1
#> [4] fastMatMR_1.2.5 testthat_3.1.10
#>
#> loaded via a namespace (and not attached):
#> [1] gtable_0.3.4 xfun_0.40 htmlwidgets_1.6.2 devtools_2.4.5
#> [5] remotes_2.4.2.1 processx_3.8.2 lattice_0.21-8 callr_3.7.3
#> [9] generics_0.1.3 vctrs_0.6.3 tools_4.3.1 ps_1.7.5
#> [13] parallel_4.3.1 tibble_3.2.1 fansi_1.0.4 highr_0.10
#> [17] pkgconfig_2.0.3 desc_1.4.2 lifecycle_1.0.3 farver_2.1.1
#> [21] compiler_4.3.1 stringr_1.5.0 brio_1.1.3 munsell_0.5.0
#> [25] decor_1.0.2 httpuv_1.6.11 htmltools_0.5.6 usethis_2.2.2
#> [29] later_1.3.1 pillar_1.9.0 crayon_1.5.2 urlchecker_1.0.1
#> [33] ellipsis_0.3.2 cachem_1.0.8 sessioninfo_1.2.2 nlme_3.1-162
#> [37] mime_0.12 commonmark_1.9.0 tidyselect_1.2.0 digest_0.6.33
#> [41] stringi_1.7.12 dplyr_1.1.2 purrr_1.0.2 labeling_0.4.3
#> [45] splines_4.3.1 rprojroot_2.0.3 fastmap_1.1.1 grid_4.3.1
#> [49] colorspace_2.1-0 cli_3.6.1 magrittr_2.0.3 pkgbuild_1.4.2
#> [53] utf8_1.2.3 withr_2.5.0 prettyunits_1.1.1 scales_1.2.1
#> [57] promises_1.2.1 cpp11_0.4.6 roxygen2_7.2.3 memoise_2.0.1
#> [61] shiny_1.7.5 evaluate_0.21 knitr_1.43 miniUI_0.1.1.1
#> [65] mgcv_1.8-42 profvis_0.3.8 rlang_1.1.1 Rcpp_1.0.11
#> [69] xtable_1.8-4 glue_1.6.2 xml2_1.3.5 pkgload_1.3.2.1
#> [73] rstudioapi_0.15.0 R6_2.5.1 fs_1.6.3
```
